Considering the overwhelming pressure on worldwide demand of fossil fuels and the climate change caused by air pollution, hybrid electric vehicles have seen a promising future thanks to the development of renewable energy sources. Among various kinds of energy sources that have been used in hybrid electric vehicles, lithium-ion battery and proton exchange membrane (PEM) fuel cell exist to be the most favorable ones owing to their high energy density and power density. However, the degradation issues of the energy sources tend to be neglected when designing the energy management strategies for the hybrid electric vehicles. Concerning existing literature, degradation modelling methods of lithium-ion batteries and PEM fuel cells are reviewed and the possibility of integrating them into health-conscious energy management is discussed. Besides, a variety of energy management strategies that have taken the influence of degradations into consideration are reviewed and classified. The contribution of this paper is to investigate the possibility of developing a health-conscious energy management strategy based on accurate estimation of degradation to improve the durability of the system.